A remark on boundary Schwarz lemma for the convex domain of finite type

Abstract

Let Ω be a bounded convex domain of finite type with smooth boundary. If f is a holomorphic self-mapping of Ω which fixes a boundary point P, we obtain some estimates of the eigenvalues of the complex Jacobian matrix of f at P. These estimates can be thought of as a generalization of the boundary Schwarz lemma on strongly pseudoconvex domains.